Uniformization (Set Theory)
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In set theory, the axiom of uniformization, a weak form of the axiom of choice, states that if R is a subset of Xtimes Y, where X and Y are Polish spaces, then there is a subset f of R that is a partial function from X to Y, and whose domain (in the sense of the set of all x such that f(x) exists) equals {xin X exists yin Y (x,y)in R},Such a function is called a uniformizing function for R, or a uniformization of R.To see the relationship with the axiom of choice,…mehr

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In set theory, the axiom of uniformization, a weak form of the axiom of choice, states that if R is a subset of Xtimes Y, where X and Y are Polish spaces, then there is a subset f of R that is a partial function from X to Y, and whose domain (in the sense of the set of all x such that f(x) exists) equals {xin X exists yin Y (x,y)in R},Such a function is called a uniformizing function for R, or a uniformization of R.To see the relationship with the axiom of choice, observe that R can be thought of as associating, to each element of X, a subset of Y. A uniformization of R then picks exactly one element from each such subset, whenever the subset is nonempty. Thus, allowing arbitrary sets X and Y (rather than just Polish spaces) would make the axiom of uniformization equivalent to AC.